Question

cho 2016a+b+c+d/a=a+2016b+c+d/b=a+b+2016c+d/c=a+b+c+2016d/d tính M=a+b/c+d + c+d/d+a + c+d/a+b + d+a/b+c

Answer 1

\(\frac{2016a+b+c+d}{a}=\frac{a+2016b+c+d}{b}=\frac{a+b+2016c+d}{c}=\frac{a+b+c+2016d}{d}\)

\(\Rightarrow\frac{2016a}{a}+\frac{b+c+d}{a}=\frac{2016b}{b}+\frac{a+c+d}{b}=\frac{2016c}{c}+\frac{a+b+d}{c}=\frac{2016d}{d}+\frac{a+b+c}{d}\)

\(\Rightarrow2016+\frac{b+c+d}{a}+1=2016+\frac{a+c+d}{b}+1=2016+\frac{a+b+d}{c}+1=2016+\frac{a+b+c}{d}+1\)

\(\Rightarrow\frac{a+b+c+d}{a}=\frac{a+b+c+d}{b}=\frac{a+b+c+d}{c}=\frac{a+b+c+d}{d}\)

\(\Rightarrow a=b=c=d\)

\(Khiđó:M=1+1+1+1=4\)